Question

the sides of a triangle measure 13 cm, 26 cm, and 15 cm. find its area. write your answer as an integer or as a decimal rounded to the nearest tenth. cm²

Explanation:

Step1: Calculate semi - perimeter

Let \(a = 13\), \(b = 26\), \(c = 15\). The semi - perimeter \(s=\frac{a + b + c}{2}=\frac{13+26 + 15}{2}=\frac{54}{2}=27\) cm.

Step2: Apply Heron's formula

The area \(A=\sqrt{s(s - a)(s - b)(s - c)}\). Substitute \(s = 27\), \(a = 13\), \(b = 26\), \(c = 15\) into the formula: \(A=\sqrt{27(27 - 13)(27 - 26)(27 - 15)}=\sqrt{27\times14\times1\times12}\). Simplify: \(27 = 3^3\), \(14=2\times7\), \(12 = 2^2\times3\). Then \(A=\sqrt{3^3\times2\times7\times1\times2^2\times3}=\sqrt{3^4\times2^3\times7}=3^2\times2\sqrt{2\times7}=9\times2\sqrt{14}=18\sqrt{14}\approx18\times3.742 = 67.4\) \(cm^2\).

Answer:

67.4